%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP720+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:31:19 AM UTC 2026
% Result : Theorem 33.68s 10.31s
% Output : CNFRefutation 33.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 7
% Syntax : Number of formulae : 117 ( 117 unt; 0 def)
% Number of atoms : 117 ( 116 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 18 ( 18 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 264 ( 0 sgn 18 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f01,axiom,
! [A] : mult(A,unit) = A,
file('theBenchmark.p',f01) ).
fof(f02,axiom,
! [A] : mult(unit,A) = A,
file('theBenchmark.p',f02) ).
fof(f03,axiom,
! [B,A] : mult(A,ld(A,B)) = B,
file('theBenchmark.p',f03) ).
fof(f04,axiom,
! [B,A] : ld(A,mult(A,B)) = B,
file('theBenchmark.p',f04) ).
fof(f05,axiom,
! [B,A] : mult(A,B) = mult(B,A),
file('theBenchmark.p',f05) ).
fof(f06,axiom,
! [D,C,B,A] : ld(mult(A,B),mult(A,mult(B,mult(C,D)))) = mult(ld(mult(A,B),mult(A,mult(B,C))),ld(mult(A,B),mult(A,mult(B,D)))),
file('theBenchmark.p',f06) ).
fof(goals,conjecture,
! [X0,X1] :
? [X2] : mult(mult(X0,X0),mult(X1,X1)) = mult(X2,X2),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0,X1] :
? [X2] : mult(mult(X0,X0),mult(X1,X1)) = mult(X2,X2),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_9,plain,
mult(A,unit) = A,
inference(clausify,[status(thm)],[f01]) ).
cnf(c_10,plain,
mult(unit,A) = A,
inference(clausify,[status(thm)],[f02]) ).
cnf(c_11,plain,
mult(A,ld(A,B)) = B,
inference(clausify,[status(thm)],[f03]) ).
cnf(c_12,plain,
ld(A,mult(A,B)) = B,
inference(clausify,[status(thm)],[f04]) ).
cnf(c_13,plain,
mult(A,B) = mult(B,A),
inference(clausify,[status(thm)],[f05]) ).
cnf(c_14,plain,
ld(mult(A,B),mult(A,mult(B,mult(C,D)))) = mult(ld(mult(A,B),mult(A,mult(B,C))),ld(mult(A,B),mult(A,mult(B,D)))),
inference(clausify,[status(thm)],[f06]) ).
fof(nnf_8,plain,
? [X0,X1] :
! [X2] : mult(mult(X0,X0),mult(X1,X1)) != mult(X2,X2),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
! [X2] : mult(mult(sK0,sK0),mult(sK1,sK1)) != mult(X2,X2),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[nnf_8]) ).
cnf(c_16,negated_conjecture,
mult(mult(sK0,sK0),mult(sK1,sK1)) != mult(A,A),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_2871,plain,
A = ld(unit,A),
inference(paramod,[status(thm)],[c_11,c_10]) ).
cnf(c_17,plain,
ld(unit,A) = A,
inference(copy,[status(thm)],[c_2871]) ).
cnf(c_18,plain,
ld(A,A) = unit,
inference(paramod,[status(thm)],[c_9,c_12]) ).
cnf(c_19,plain,
ld(A,mult(B,A)) = B,
inference(paramod,[status(thm)],[c_13,c_12]) ).
cnf(c_20,plain,
mult(mult(A,B),mult(ld(mult(A,B),mult(A,mult(B,C))),ld(mult(A,B),mult(A,mult(B,D))))) = mult(A,mult(B,mult(C,D))),
inference(paramod,[status(thm)],[c_14,c_11]) ).
cnf(c_2872,plain,
ld(mult(A,B),mult(A,mult(B,C))) = mult(ld(mult(A,B),mult(A,mult(B,D))),ld(mult(A,B),mult(A,mult(B,ld(D,C))))),
inference(paramod,[status(thm)],[c_11,c_14]) ).
cnf(c_22,plain,
mult(ld(mult(A,B),mult(A,mult(B,C))),ld(mult(A,B),mult(A,mult(B,ld(C,D))))) = ld(mult(A,B),mult(A,mult(B,D))),
inference(copy,[status(thm)],[c_2872]) ).
cnf(c_24,plain,
ld(mult(A,B),mult(A,mult(mult(C,D),B))) = mult(ld(mult(A,B),mult(A,mult(B,C))),ld(mult(A,B),mult(A,mult(B,D)))),
inference(paramod,[status(thm)],[c_13,c_14]) ).
cnf(c_27,plain,
ld(ld(A,B),B) = A,
inference(paramod,[status(thm)],[c_11,c_19]) ).
cnf(c_2873,plain,
mult(ld(mult(A,B),mult(A,mult(B,B))),ld(mult(A,B),mult(A,C))) = ld(mult(A,B),mult(A,mult(B,C))),
inference(paramod,[status(thm)],[c_11,c_22]) ).
cnf(c_31,plain,
ld(mult(A,B),mult(A,mult(B,C))) = mult(ld(mult(A,B),mult(A,mult(B,B))),ld(mult(A,B),mult(A,C))),
inference(copy,[status(thm)],[c_2873]) ).
cnf(c_2874,plain,
mult(ld(mult(A,B),mult(A,mult(B,C))),ld(mult(B,A),mult(A,mult(B,ld(C,D))))) = ld(mult(A,B),mult(A,mult(B,D))),
inference(paramod,[status(thm)],[c_13,c_22]) ).
cnf(c_36,plain,
ld(mult(A,B),mult(A,mult(B,C))) = mult(ld(mult(A,B),mult(A,mult(B,D))),ld(mult(B,A),mult(A,mult(B,ld(D,C))))),
inference(copy,[status(thm)],[c_2874]) ).
cnf(c_2875,plain,
mult(A,ld(mult(A,A),mult(A,mult(A,ld(A,B))))) = ld(mult(A,A),mult(A,mult(A,B))),
inference(paramod,[status(thm)],[c_19,c_22]) ).
cnf(c_2876,plain,
mult(A,ld(mult(A,A),mult(A,B))) = ld(mult(A,A),mult(A,mult(A,B))),
inference(paramod,[status(thm)],[c_11,c_2875]) ).
cnf(c_39,plain,
ld(mult(A,A),mult(A,mult(A,B))) = mult(A,ld(mult(A,A),mult(A,B))),
inference(copy,[status(thm)],[c_2876]) ).
cnf(c_2877,plain,
ld(mult(A,A),mult(A,A)) = mult(A,ld(mult(A,A),mult(A,unit))),
inference(paramod,[status(thm)],[c_9,c_39]) ).
cnf(c_2878,plain,
unit = mult(A,ld(mult(A,A),mult(A,unit))),
inference(paramod,[status(thm)],[c_18,c_2877]) ).
cnf(c_2879,plain,
unit = mult(A,ld(mult(A,A),A)),
inference(paramod,[status(thm)],[c_9,c_2878]) ).
cnf(c_42,plain,
mult(A,ld(mult(A,A),A)) = unit,
inference(copy,[status(thm)],[c_2879]) ).
cnf(c_2880,plain,
ld(A,unit) = ld(mult(A,A),A),
inference(paramod,[status(thm)],[c_42,c_12]) ).
cnf(c_50,plain,
ld(mult(A,A),A) = ld(A,unit),
inference(copy,[status(thm)],[c_2880]) ).
cnf(c_2881,plain,
mult(ld(mult(A,B),mult(A,mult(B,mult(B,B)))),ld(mult(A,B),mult(A,unit))) = ld(mult(A,B),mult(A,mult(B,B))),
inference(paramod,[status(thm)],[c_42,c_22]) ).
cnf(c_2882,plain,
mult(mult(ld(mult(A,B),mult(A,mult(B,B))),ld(mult(A,B),mult(A,mult(B,B)))),ld(mult(A,B),mult(A,unit))) = ld(mult(A,B),mult(A,mult(B,B))),
inference(paramod,[status(thm)],[c_14,c_2881]) ).
cnf(c_2883,plain,
mult(mult(ld(mult(A,B),mult(A,mult(B,B))),ld(mult(A,B),mult(A,mult(B,B)))),ld(mult(A,B),A)) = ld(mult(A,B),mult(A,mult(B,B))),
inference(paramod,[status(thm)],[c_9,c_2882]) ).
cnf(c_53,plain,
mult(ld(mult(A,B),A),mult(ld(mult(A,B),mult(A,mult(B,B))),ld(mult(A,B),mult(A,mult(B,B))))) = ld(mult(A,B),mult(A,mult(B,B))),
inference(paramod,[status(thm)],[c_13,c_2883]) ).
cnf(c_54,plain,
mult(mult(A,A),ld(A,unit)) = A,
inference(paramod,[status(thm)],[c_50,c_11]) ).
cnf(c_2884,plain,
mult(mult(ld(A,unit),ld(A,unit)),A) = ld(A,unit),
inference(paramod,[status(thm)],[c_27,c_54]) ).
cnf(c_57,plain,
mult(A,mult(ld(A,unit),ld(A,unit))) = ld(A,unit),
inference(paramod,[status(thm)],[c_13,c_2884]) ).
cnf(c_2885,plain,
mult(A,mult(ld(mult(B,ld(B,A)),mult(B,mult(ld(B,A),C))),ld(mult(B,ld(B,A)),mult(B,mult(ld(B,A),D))))) = mult(B,mult(ld(B,A),mult(C,D))),
inference(paramod,[status(thm)],[c_11,c_20]) ).
cnf(c_2886,plain,
mult(A,mult(ld(A,mult(B,mult(ld(B,A),C))),ld(mult(B,ld(B,A)),mult(B,mult(ld(B,A),D))))) = mult(B,mult(ld(B,A),mult(C,D))),
inference(paramod,[status(thm)],[c_11,c_2885]) ).
cnf(c_60,plain,
mult(A,mult(ld(A,mult(B,mult(ld(B,A),C))),ld(A,mult(B,mult(ld(B,A),D))))) = mult(B,mult(ld(B,A),mult(C,D))),
inference(paramod,[status(thm)],[c_11,c_2886]) ).
cnf(c_2887,plain,
mult(mult(sK0,sK0),mult(sK1,sK1)) != ld(mult(A,B),mult(A,mult(mult(C,C),B))),
inference(paramod,[status(thm)],[c_24,c_16]) ).
cnf(c_85,plain,
ld(mult(A,B),mult(A,mult(mult(C,C),B))) != mult(mult(sK0,sK0),mult(sK1,sK1)),
inference(copy,[status(thm)],[c_2887]) ).
cnf(c_93,plain,
ld(mult(A,ld(mult(B,B),C)),mult(A,C)) != mult(mult(sK0,sK0),mult(sK1,sK1)),
inference(paramod,[status(thm)],[c_11,c_85]) ).
cnf(c_102,plain,
ld(mult(ld(mult(A,A),B),C),mult(C,B)) != mult(mult(sK0,sK0),mult(sK1,sK1)),
inference(paramod,[status(thm)],[c_13,c_93]) ).
cnf(c_188,plain,
ld(mult(ld(A,unit),B),mult(B,A)) != mult(mult(sK0,sK0),mult(sK1,sK1)),
inference(paramod,[status(thm)],[c_50,c_102]) ).
cnf(c_197,plain,
ld(mult(ld(A,unit),B),mult(A,B)) != mult(mult(sK0,sK0),mult(sK1,sK1)),
inference(paramod,[status(thm)],[c_13,c_188]) ).
cnf(c_202,plain,
ld(mult(ld(A,unit),ld(A,B)),B) != mult(mult(sK0,sK0),mult(sK1,sK1)),
inference(paramod,[status(thm)],[c_11,c_197]) ).
cnf(c_2888,plain,
ld(mult(A,B),mult(A,ld(B,unit))) = mult(ld(mult(A,B),mult(A,mult(B,ld(B,unit)))),ld(mult(A,B),mult(A,mult(B,ld(B,unit))))),
inference(paramod,[status(thm)],[c_57,c_14]) ).
cnf(c_2889,plain,
ld(mult(A,B),mult(A,ld(B,unit))) = mult(ld(mult(A,B),mult(A,unit)),ld(mult(A,B),mult(A,mult(B,ld(B,unit))))),
inference(paramod,[status(thm)],[c_11,c_2888]) ).
cnf(c_2890,plain,
ld(mult(A,B),mult(A,ld(B,unit))) = mult(ld(mult(A,B),A),ld(mult(A,B),mult(A,mult(B,ld(B,unit))))),
inference(paramod,[status(thm)],[c_9,c_2889]) ).
cnf(c_2891,plain,
ld(mult(A,B),mult(A,ld(B,unit))) = mult(ld(mult(A,B),A),ld(mult(A,B),mult(A,unit))),
inference(paramod,[status(thm)],[c_11,c_2890]) ).
cnf(c_207,plain,
ld(mult(A,B),mult(A,ld(B,unit))) = mult(ld(mult(A,B),A),ld(mult(A,B),A)),
inference(paramod,[status(thm)],[c_9,c_2891]) ).
cnf(c_2892,plain,
mult(ld(mult(A,ld(A,unit)),ld(A,unit)),ld(mult(A,ld(A,unit)),mult(A,mult(ld(A,unit),ld(ld(A,unit),B))))) = ld(mult(A,ld(A,unit)),mult(A,mult(ld(A,unit),B))),
inference(paramod,[status(thm)],[c_57,c_22]) ).
cnf(c_2893,plain,
mult(ld(unit,ld(A,unit)),ld(mult(A,ld(A,unit)),mult(A,mult(ld(A,unit),ld(ld(A,unit),B))))) = ld(mult(A,ld(A,unit)),mult(A,mult(ld(A,unit),B))),
inference(paramod,[status(thm)],[c_11,c_2892]) ).
cnf(c_2894,plain,
mult(ld(A,unit),ld(mult(A,ld(A,unit)),mult(A,mult(ld(A,unit),ld(ld(A,unit),B))))) = ld(mult(A,ld(A,unit)),mult(A,mult(ld(A,unit),B))),
inference(paramod,[status(thm)],[c_17,c_2893]) ).
cnf(c_2895,plain,
mult(ld(A,unit),ld(unit,mult(A,mult(ld(A,unit),ld(ld(A,unit),B))))) = ld(mult(A,ld(A,unit)),mult(A,mult(ld(A,unit),B))),
inference(paramod,[status(thm)],[c_11,c_2894]) ).
cnf(c_2896,plain,
mult(ld(A,unit),ld(unit,mult(A,B))) = ld(mult(A,ld(A,unit)),mult(A,mult(ld(A,unit),B))),
inference(paramod,[status(thm)],[c_11,c_2895]) ).
cnf(c_2897,plain,
mult(ld(A,unit),mult(A,B)) = ld(mult(A,ld(A,unit)),mult(A,mult(ld(A,unit),B))),
inference(paramod,[status(thm)],[c_17,c_2896]) ).
cnf(c_2898,plain,
mult(ld(A,unit),mult(A,B)) = ld(unit,mult(A,mult(ld(A,unit),B))),
inference(paramod,[status(thm)],[c_11,c_2897]) ).
cnf(c_209,plain,
mult(ld(A,unit),mult(A,B)) = mult(A,mult(ld(A,unit),B)),
inference(paramod,[status(thm)],[c_17,c_2898]) ).
cnf(c_238,plain,
ld(mult(A,B),mult(B,ld(A,unit))) = mult(ld(mult(B,A),B),ld(mult(B,A),B)),
inference(paramod,[status(thm)],[c_13,c_207]) ).
cnf(c_340,plain,
ld(mult(A,B),mult(B,ld(A,unit))) = mult(ld(mult(A,B),B),ld(mult(B,A),B)),
inference(paramod,[status(thm)],[c_13,c_238]) ).
cnf(c_426,plain,
ld(mult(ld(mult(A,B),B),ld(mult(B,A),B)),mult(B,ld(A,unit))) = mult(A,B),
inference(paramod,[status(thm)],[c_340,c_27]) ).
cnf(c_2899,plain,
ld(mult(A,B),mult(A,B)) = mult(ld(mult(A,B),mult(A,mult(B,C))),ld(mult(B,A),mult(A,mult(B,ld(C,unit))))),
inference(paramod,[status(thm)],[c_9,c_36]) ).
cnf(c_2900,plain,
unit = mult(ld(mult(A,B),mult(A,mult(B,C))),ld(mult(B,A),mult(A,mult(B,ld(C,unit))))),
inference(paramod,[status(thm)],[c_18,c_2899]) ).
cnf(c_505,plain,
mult(ld(mult(A,B),mult(A,mult(B,C))),ld(mult(B,A),mult(A,mult(B,ld(C,unit))))) = unit,
inference(copy,[status(thm)],[c_2900]) ).
cnf(c_2901,plain,
ld(mult(A,B),mult(B,mult(A,C))) = mult(ld(mult(B,A),mult(B,mult(A,D))),ld(mult(A,B),mult(B,mult(A,ld(D,C))))),
inference(paramod,[status(thm)],[c_13,c_36]) ).
cnf(c_507,plain,
mult(ld(mult(A,B),mult(A,mult(B,C))),ld(mult(B,A),mult(A,mult(B,ld(C,D))))) = ld(mult(B,A),mult(A,mult(B,D))),
inference(copy,[status(thm)],[c_2901]) ).
cnf(c_2902,plain,
ld(mult(B,A),mult(A,mult(B,unit))) = unit,
inference(paramod,[status(thm)],[c_507,c_505]) ).
cnf(c_519,plain,
ld(mult(A,B),mult(B,A)) = unit,
inference(paramod,[status(thm)],[c_9,c_2902]) ).
cnf(c_2903,plain,
mult(ld(A,unit),B) = mult(A,mult(ld(A,unit),ld(A,B))),
inference(paramod,[status(thm)],[c_11,c_209]) ).
cnf(c_550,plain,
mult(A,mult(ld(A,unit),ld(A,B))) = mult(ld(A,unit),B),
inference(copy,[status(thm)],[c_2903]) ).
cnf(c_584,plain,
ld(A,mult(ld(A,unit),B)) = mult(ld(A,unit),ld(A,B)),
inference(paramod,[status(thm)],[c_550,c_12]) ).
cnf(c_587,plain,
ld(mult(ld(A,unit),ld(A,B)),mult(ld(A,unit),B)) = A,
inference(paramod,[status(thm)],[c_550,c_19]) ).
cnf(c_2904,plain,
ld(ld(A,unit),mult(A,B)) = mult(ld(ld(A,unit),unit),ld(ld(A,unit),B)),
inference(paramod,[status(thm)],[c_27,c_584]) ).
cnf(c_633,plain,
ld(ld(A,unit),mult(A,B)) = mult(A,ld(ld(A,unit),B)),
inference(paramod,[status(thm)],[c_27,c_2904]) ).
cnf(c_660,plain,
ld(mult(ld(A,unit),ld(A,B)),mult(B,ld(A,unit))) = A,
inference(paramod,[status(thm)],[c_13,c_587]) ).
cnf(c_770,plain,
ld(mult(ld(A,unit),B),mult(mult(B,A),ld(A,unit))) = A,
inference(paramod,[status(thm)],[c_19,c_660]) ).
cnf(c_2905,plain,
ld(mult(A,B),mult(mult(B,ld(A,unit)),ld(ld(A,unit),unit))) = ld(A,unit),
inference(paramod,[status(thm)],[c_27,c_770]) ).
cnf(c_2906,plain,
ld(mult(A,B),mult(mult(B,ld(A,unit)),A)) = ld(A,unit),
inference(paramod,[status(thm)],[c_27,c_2905]) ).
cnf(c_940,plain,
ld(mult(A,B),mult(A,mult(B,ld(A,unit)))) = ld(A,unit),
inference(paramod,[status(thm)],[c_13,c_2906]) ).
cnf(c_2907,plain,
mult(mult(A,B),mult(ld(mult(A,B),mult(mult(B,A),mult(unit,C))),ld(mult(A,B),mult(mult(B,A),mult(ld(mult(B,A),mult(A,B)),D))))) = mult(mult(B,A),mult(ld(mult(B,A),mult(A,B)),mult(C,D))),
inference(paramod,[status(thm)],[c_519,c_60]) ).
cnf(c_2908,plain,
mult(mult(A,B),mult(ld(mult(A,B),mult(mult(B,A),C)),ld(mult(A,B),mult(mult(B,A),mult(ld(mult(B,A),mult(A,B)),D))))) = mult(mult(B,A),mult(ld(mult(B,A),mult(A,B)),mult(C,D))),
inference(paramod,[status(thm)],[c_10,c_2907]) ).
cnf(c_2909,plain,
mult(mult(A,B),mult(ld(mult(A,B),mult(mult(B,A),C)),ld(mult(A,B),mult(mult(B,A),mult(unit,D))))) = mult(mult(B,A),mult(ld(mult(B,A),mult(A,B)),mult(C,D))),
inference(paramod,[status(thm)],[c_519,c_2908]) ).
cnf(c_2910,plain,
mult(mult(A,B),mult(ld(mult(A,B),mult(mult(B,A),C)),ld(mult(A,B),mult(mult(B,A),D)))) = mult(mult(B,A),mult(ld(mult(B,A),mult(A,B)),mult(C,D))),
inference(paramod,[status(thm)],[c_10,c_2909]) ).
cnf(c_2911,plain,
mult(mult(A,B),mult(ld(mult(A,B),mult(mult(B,A),C)),ld(mult(A,B),mult(mult(B,A),D)))) = mult(mult(B,A),mult(unit,mult(C,D))),
inference(paramod,[status(thm)],[c_519,c_2910]) ).
cnf(c_1172,plain,
mult(mult(A,B),mult(ld(mult(A,B),mult(mult(B,A),C)),ld(mult(A,B),mult(mult(B,A),D)))) = mult(mult(B,A),mult(C,D)),
inference(paramod,[status(thm)],[c_10,c_2911]) ).
cnf(c_2912,plain,
ld(A,unit) = mult(ld(mult(A,B),mult(A,mult(B,B))),ld(mult(A,B),mult(A,ld(A,unit)))),
inference(paramod,[status(thm)],[c_940,c_31]) ).
cnf(c_2913,plain,
ld(A,unit) = mult(ld(mult(A,B),mult(A,mult(B,B))),ld(mult(A,B),unit)),
inference(paramod,[status(thm)],[c_11,c_2912]) ).
cnf(c_2914,plain,
ld(A,unit) = mult(ld(mult(A,B),unit),ld(mult(A,B),mult(A,mult(B,B)))),
inference(paramod,[status(thm)],[c_13,c_2913]) ).
cnf(c_1404,plain,
mult(ld(mult(A,B),unit),ld(mult(A,B),mult(A,mult(B,B)))) = ld(A,unit),
inference(copy,[status(thm)],[c_2914]) ).
cnf(c_2915,plain,
ld(mult(ld(ld(mult(A,B),mult(A,mult(B,B))),mult(ld(mult(A,B),mult(A,mult(B,B))),ld(mult(A,B),mult(A,mult(B,B))))),ld(mult(mult(ld(mult(A,B),mult(A,mult(B,B))),ld(mult(A,B),mult(A,mult(B,B)))),ld(mult(A,B),A)),mult(ld(mult(A,B),mult(A,mult(B,B))),ld(mult(A,B),mult(A,mult(B,B)))))),mult(mult(ld(mult(A,B),mult(A,mult(B,B))),ld(mult(A,B),mult(A,mult(B,B)))),ld(ld(mult(A,B),A),unit))) = mult(ld(mult(A,B),A),mult(ld(mult(A,B),mult(A,mult(B,B))),ld(mult(A,B),mult(A,mult(B,B))))),
inference(paramod,[status(thm)],[c_53,c_426]) ).
cnf(c_2916,plain,
ld(mult(ld(mult(A,B),mult(A,mult(B,B))),ld(mult(mult(ld(mult(A,B),mult(A,mult(B,B))),ld(mult(A,B),mult(A,mult(B,B)))),ld(mult(A,B),A)),mult(ld(mult(A,B),mult(A,mult(B,B))),ld(mult(A,B),mult(A,mult(B,B)))))),mult(mult(ld(mult(A,B),mult(A,mult(B,B))),ld(mult(A,B),mult(A,mult(B,B)))),ld(ld(mult(A,B),A),unit))) = mult(ld(mult(A,B),A),mult(ld(mult(A,B),mult(A,mult(B,B))),ld(mult(A,B),mult(A,mult(B,B))))),
inference(paramod,[status(thm)],[c_12,c_2915]) ).
cnf(c_2917,plain,
ld(mult(ld(mult(A,B),mult(A,mult(B,B))),ld(mult(ld(mult(A,B),A),mult(ld(mult(A,B),mult(A,mult(B,B))),ld(mult(A,B),mult(A,mult(B,B))))),mult(ld(mult(A,B),mult(A,mult(B,B))),ld(mult(A,B),mult(A,mult(B,B)))))),mult(mult(ld(mult(A,B),mult(A,mult(B,B))),ld(mult(A,B),mult(A,mult(B,B)))),ld(ld(mult(A,B),A),unit))) = mult(ld(mult(A,B),A),mult(ld(mult(A,B),mult(A,mult(B,B))),ld(mult(A,B),mult(A,mult(B,B))))),
inference(paramod,[status(thm)],[c_13,c_2916]) ).
cnf(c_2918,plain,
ld(mult(ld(mult(A,B),mult(A,mult(B,B))),ld(ld(mult(A,B),mult(A,mult(B,B))),mult(ld(mult(A,B),mult(A,mult(B,B))),ld(mult(A,B),mult(A,mult(B,B)))))),mult(mult(ld(mult(A,B),mult(A,mult(B,B))),ld(mult(A,B),mult(A,mult(B,B)))),ld(ld(mult(A,B),A),unit))) = mult(ld(mult(A,B),A),mult(ld(mult(A,B),mult(A,mult(B,B))),ld(mult(A,B),mult(A,mult(B,B))))),
inference(paramod,[status(thm)],[c_53,c_2917]) ).
cnf(c_2919,plain,
ld(mult(ld(mult(A,B),mult(A,mult(B,B))),ld(mult(A,B),mult(A,mult(B,B)))),mult(mult(ld(mult(A,B),mult(A,mult(B,B))),ld(mult(A,B),mult(A,mult(B,B)))),ld(ld(mult(A,B),A),unit))) = mult(ld(mult(A,B),A),mult(ld(mult(A,B),mult(A,mult(B,B))),ld(mult(A,B),mult(A,mult(B,B))))),
inference(paramod,[status(thm)],[c_12,c_2918]) ).
cnf(c_2920,plain,
ld(ld(mult(A,B),A),unit) = mult(ld(mult(A,B),A),mult(ld(mult(A,B),mult(A,mult(B,B))),ld(mult(A,B),mult(A,mult(B,B))))),
inference(paramod,[status(thm)],[c_12,c_2919]) ).
cnf(c_1616,plain,
ld(ld(mult(A,B),A),unit) = ld(mult(A,B),mult(A,mult(B,B))),
inference(paramod,[status(thm)],[c_53,c_2920]) ).
cnf(c_2921,plain,
ld(ld(A,B),unit) = ld(mult(B,ld(B,A)),mult(B,mult(ld(B,A),ld(B,A)))),
inference(paramod,[status(thm)],[c_11,c_1616]) ).
cnf(c_2026,plain,
ld(ld(A,B),unit) = ld(A,mult(B,mult(ld(B,A),ld(B,A)))),
inference(paramod,[status(thm)],[c_11,c_2921]) ).
cnf(c_2922,plain,
ld(ld(A,unit),mult(A,mult(B,B))) != mult(mult(sK0,sK0),mult(sK1,sK1)),
inference(paramod,[status(thm)],[c_1404,c_202]) ).
cnf(c_2670,plain,
mult(A,ld(ld(A,unit),mult(B,B))) != mult(mult(sK0,sK0),mult(sK1,sK1)),
inference(paramod,[status(thm)],[c_633,c_2922]) ).
cnf(c_2859,plain,
mult(ld(A,unit),ld(A,mult(B,B))) != mult(mult(sK0,sK0),mult(sK1,sK1)),
inference(paramod,[status(thm)],[c_27,c_2670]) ).
cnf(c_2923,plain,
mult(ld(ld(A,mult(B,B)),unit),A) != mult(mult(sK0,sK0),mult(sK1,sK1)),
inference(paramod,[status(thm)],[c_27,c_2859]) ).
cnf(c_2924,plain,
mult(ld(A,mult(mult(B,B),mult(ld(mult(B,B),A),ld(mult(B,B),A)))),A) != mult(mult(sK0,sK0),mult(sK1,sK1)),
inference(paramod,[status(thm)],[c_2026,c_2923]) ).
cnf(c_2925,plain,
mult(A,ld(A,mult(mult(B,B),mult(ld(mult(B,B),A),ld(mult(B,B),A))))) != mult(mult(sK0,sK0),mult(sK1,sK1)),
inference(paramod,[status(thm)],[c_13,c_2924]) ).
cnf(c_2869,plain,
mult(mult(A,A),mult(ld(mult(A,A),B),ld(mult(A,A),B))) != mult(mult(sK0,sK0),mult(sK1,sK1)),
inference(paramod,[status(thm)],[c_11,c_2925]) ).
cnf(c_2870,plain,
$false,
inference(resolve,[status(thm)],[c_2869,c_1172]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP720+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/5.44 % Computer : n016.cluster.edu
% 0.16/5.44 % Model : x86_64 x86_64
% 0.16/5.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.44 % Memory : 8046.5625MB
% 0.16/5.44 % OS : Linux 6.8.0-71-generic
% 0.16/5.44 % CPULimit : 300
% 0.16/5.44 % WCLimit : 300
% 0.16/5.44 % DateTime : Fri Sep 25 15:45:35 UTC 2026
% 0.16/5.45 % CPUTime :
% 0.16/5.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/5.45 % Process 2777320 was started by sandbox on n016,
% 0.16/5.45 % Fri Sep 25 15:45:35 2026
% 0.16/5.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.16/5.46
% 0.16/5.46 % From the command line: assign(max_seconds, 300).
% 33.68/10.31
% 33.68/10.31 % SZS status Theorem for theBenchmark
% 33.68/10.31
% 33.68/10.31 % Proof 1 at 4.21 (+ 0.59) seconds.
% 33.68/10.31 % Length of proof is 59.
% 33.68/10.31 % Level of proof is 18.
% 33.68/10.31 % Maximum clause weight is 91.000.
% 33.68/10.31 % Given clauses 217.
% 33.68/10.31
% 33.68/10.31 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------